Abstract
In this study we examine the electronic and molecular structures of the [51 knot···(PF6)10]+ pentafoil knot system and report calculated interaction energies that result from halides (X = F, Cl, Br, and I) localized at the center of the [51knot···(PF6)9]X molecular structure. The equilibrium geometries were fully optimized at the ONIOM(M06/6-31G(2d,p):PM6) level of theory, starting from an initial geometry for the pentafoil knot obtained from experimental X-ray data. The molecular systems were divided into two layers, for which the M06/6-31G(2d,p) level of theory was used to describe the high layer ([C4H6]5X- structure) and the PM6 semiempirical method was employed for the low layer. The calculated electronic energies show that the interaction between the fluorine anion and the pentafoil knot produces the most stable structure, whereas an unfavorable interaction is observed for iodide due to the diffuse character of its electronic cloud. Using basis set superposition error (BSSE) correction techniques, the observed values of the interaction are -0.201 hartrees for the fluoride ion and -0.100 hartrees for iodide.
Highlights
Knot theory has been developed by mathematicians and physicists since the 18th century and knotted chemical structures remain bizarre for chemists, several knots are already well-known and characterized
Using DFT and semiempirical quantum chemical methods with an ONIOM approach (M06/6-31G(2d,p):PM6), we have studied the interactions between the halides X = F, Cl, Br, I and a pentafoil [51 knot···(PF6)10]+
From the equilibrium geometries fully optimized by the ONIOM method, we have obtained excellent results for values of the bond distance, bond angle, and dihedral angle along the molecular structure when these variables are compared with the results obtained from X-ray data
Summary
Knot theory has been developed by mathematicians and physicists since the 18th century and knotted chemical structures remain bizarre for chemists, several knots are already well-known and characterized. Knotted structures occur in nature as knotted proteins,[1,2,3] DNA,[4] and organic molecules.[5] Knots, links, graphs, and various other topological isomers have been discussed in monographs on chemical conformation and chirality.[6]. From a more mathematical and set-theoretic point of view, a knot is a homeomorphism (an additive and continuous function) that maps a circle into three dimensional space and cannot be reduced to the unknot (a circle).[7]. A knot is the embedding of a circle in three-dimensional Euclidean space, 3.7 In 1860, Lord Kelvin stated that atoms could be represented by knots in the aether, which led Peter Tait to create the first knot table classification.
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